Length Of Micelles Research Articles

Two-species model for nonlinear flow of wormlike micelle solutions. Part II: Experiment

Applications often expose wormlike micelle solutions to a very wide range of shear and temperature conditions. The two-species model presented in Part I [Salipante et al., J. Rheol. 68 (2024)] describes the nonlinear rheology over a wide range of shear rates. Here, we compare the model predictions to measurements using a combination of microcapillary and rotational rheology to measure the viscosity of surfactant solutions across seven decades of shear rate and five decades of viscosity. The effect of temperature is studied between 20 and 60 °C for different surfactant concentrations. Model parameters are determined from both small-amplitude shear measurements and fitting to the nonlinear data. Under shear stress, the model predicts due to hindered combination kinetics that the average micelle length decreases from several micrometers to a few hundred nanometers. At sufficiently high stress, the micelle shear rheology exhibits a transition from entangled wormlike behavior to a dilute rod rheology in agreement with the model. Transient stress-growth measurements exhibit a large overshoot, which is rather well predicted by the model with hindered combination rate. Microcapillary flow birefringence also is adequately predicted by the model, confirming the accuracy of its predicted micelle lengths and exhibiting a marked change in stress-optic response at the transition between entangled polymers and dilute rods. The relaxation of retardance after flow cessation follows model predictions that include micelle-micelle interactions, which are sensitive to the rotational diffusivity and length. These methods can be applied broadly to explore relationships between composition and performance.

Two-species model for nonlinear flow of wormlike micelle solutions. Part I: Model

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.

Effect of Electrostatic Interactions in Wormlike Micelles of Surfactants Based on Betaine and Charged Tertiary Amine with the Same Hydrophobic Groups

The viscoelastic properties and structure of solutions of mixed wormlike micelles based on a zwitterionic surfactant, oleylamidopropyldimethylcarboxybetaine (OAPB), and positively charged oleylamidopropyldimethylamine (OAPA) have been studied at different ratios between the components. At a small fraction of the cationic surfactant, OAPA, the solution exhibits viscoelastic properties characteristic of semidiluted solutions of entangled wormlike micelles, the presence of which has been confirmed by cryogenic electron microscopy data. It has been found that, as the molar fraction of the charged surfactant increases to 0.1, the viscosity and relaxation time of the solutions decrease by a factor of three, and the values of the storage modulus remain unchanged at short stress action times. The studied surfactants have a similar structure; therefore, when replacing zwitterionic OAPB molecules by positively charged OAPA molecules, the main factor of variations in the properties and structure is the enhancement of the electrostatic repulsion on the micelle surface. It has been shown that this factor leads to a decrease in the average length of micelles and an increase in their number, which have a weak effect on the rheological properties of the system as long as the length of the micelles is larger than the length of the subchains in the network. With an increase in the molar fraction of OAPA from 0.1 to 0.5, the viscosity and relaxation time drop drastically by several orders of magnitude and the viscoelastic response of the solution is lost; i.e., the network is destroyed. This transition from a semidilute solution to a dilute one is explained by a decrease in the length of the wormlike micelles and the formation of spherical ones. Cryogenic electron microscopy images have confirmed the formation of a mixture of long and short wormlike micelles with spherical micelles at an OAPA molar fraction of 0.5.

Scalable Preparation of Cylindrical Block Copolymer Micelles with a Liquid-Crystalline Perfluorinated Core by Photoinitiated Reversible Addition-Fragmentation Chain Transfer Dispersion Polymerization

One-dimensional block copolymer micelles have exhibited considerable promise in various fields. However, the large-scale preparation of one-dimensional block copolymer micelles is always challenging. Here, we report the preparation of cylindrical block copolymer micelles up to 30% w/w solids by photoinitiated reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization of 2-(perfluorooctyl)ethyl methacrylate (FMA) in ethanol. Because of the liquid-crystalline ordering effect of the PFMA core-forming block at low temperatures, cylindrical micelles could be obtained over a wide range of degree of polymerization of PFMA. The length of cylindrical micelles could be roughly controlled by changing the molar mass of the macromolecular chain transfer agent (macro-CTA). Finally, the concept of seeded growth was successfully incorporated into photoinitiated RAFT dispersion polymerization, allowing the epitaxial growth of cylindrical micelles from seeds. We expect that this method will offer considerable opportunities for the large-scale preparation of well-defined cylindrical micelles that may find applications in some specific areas.

Photo-Controlled Dynamics and Transport in Entangled Wormlike Micellar Nanocomposites Studied by XPCS

Dynamics of nanoparticles (NPs) in microscopic networks, in particular, localization and transport, play a key role in designing new functional nanocomposites and drug delivery systems. To this aim, it is crucial to understand the interplay between the network structure and dynamics on the microscopic scale which determines NP diffusion. Here, we study the localization and transport of spherical NPs in photorheological wormlike micellar nanocomposites where the mobility of the NPs is controlled by the network mesh size and the micelle length, which can be tuned by UV-illumination. The macroscopic viscoelastic properties are measured by classical rheology, while X-ray photon correlation spectroscopy and nanorheology provide information on the microscopic NP dynamics on length scales on the order of the network mesh size. On long time scales, the data reveal that transport through the network is determined by the ratio between the NP size and the network mesh size, while upon UV illumination, the NP mobility is drastically enhanced. On shorter time scales, the influence of the dynamical and structural micelle properties on the NP dynamics under confinement is explored and indicates an anomalous speed-up of the dynamics, which is discussed in the context of changes in the local structure and non-linear phenomena such as strain stiffening and hopping motion.

Modeling Micellar Growth and Branching in Mixtures of Zwitterionic with Ionic Surfactants.

Zwitterionic surfactants are widely applied as drag-reducing or thickening agents because their aggregation patterns may drastically change in response to variations of the system composition or external stimuli, which provides controllable viscoelasticity. For predicting aggregation behavior of surfactant mixtures, classical molecular thermodynamic models have been widely used. Particularly, the results of modeling have been reported for zwitterionic/ionic surfactant mixtures. However, for solutions containing a zwitterionic surfactant, no molecular thermodynamic model has been proposed for a micellar branch. In this work we extend the classical molecular thermodynamic aggregation model to describe aggregation in the aqueous mixtures that contain a zwitterionic and an ionic surfactant. We derive analytical expressions (1) for the contribution of dipoles to the electrostatic term of the standard free energy of aggregation into micellar branches and (2) for the dipolar contribution to the persistence length of wormlike micelles. The dependence of micellar branching on the surfactant concentration is taken into account by including the population of micellar branches in the material balance equations. This model is applied to predict aggregation equilibrium in aqueous salt solutions of betaine (oleoylamidopropyl-N,N-dimethylbetaine) mixed with sodium dodecyl sulfate (SDS) and the longer tail sodium n-alkyl sulfates. We discuss the predicted properties of the aggregates and micellar networks and compare our predictions with available experimental data.

Analytical modeling of micelle growth. 5. Molecular thermodynamics of micelles from zwitterionic surfactants

HypothesisThe critical micelle concentration, aggregation number, shape and length of spherocylindrical micelles in solutions of zwitterionic surfactants can be predicted by knowing the molecular parameters and surfactant concentrations. This can be achieved by upgrading the quantitative molecular thermodynamic model with expressions for the electrostatic interaction energy between the zwitterionic dipoles and micellar hydrophobic cores of spherical and cylindrical shapes. TheoryThe correct prediction of the mean micellar aggregation numbers requires precise calculations of the free energy per molecule in the micelles. New analytical expressions for the dipole electrostatic interaction energy are derived based on the exact solutions of the electrostatic problem for a single charge close to a boundary of spherical and cylindrical dielectric media. The obtained general theory is valid for arbitrary ratios between dielectric constants, radii of spheres and cylinders, positions, and orientations of dipoles. FindingsThe detailed numerical results show quantitatively the effects of the micelle curvature and dielectric properties of the continuum media on the decrease of the dipole electrostatic interaction energy. Excellent agreement was achieved between the theoretical predictions and experimental data for the critical micelle concentration, size and aggregation number of zwitterionic surfactant micelles. This study can be extended to mixed micelles of zwitterionic and ionic surfactants in the presence of salt to interpret and predict the synergistic effect on the rheology of solutions.

The effect and enhancement mechanism of hydrophobic interaction and electrostatic interaction on zwitterionic wormlike micelles

The effects of hydrophobic interaction and electrostatic interaction on the structure of zwitterionic wormlike micelles (WLMs) were studied. The change of the hydrocarbon chain length and addition of cetyl trimethyl ammonium chloride (CTAC) were employed to explore the effect of hydrophobic interaction and electrostatic interaction on the wormlike micelles constructed by zwitterionic viscoelastic surfactants and sodium p-toluene sulfonate (NaPts). The experimental results show that increasing hydrocarbon chain length of zwitterionic surfactant and the addition of CTAC can increase the viscoelasticity and zero-shear viscosity of the system. The calculated length of wormlike micelles also increases. This shows that the enhancement of hydrophobic interaction and electrostatic interaction can promote the growth and entanglement of wormlike micelles. In addition, scanning electron microscope (SEM) images confirmed that CTAC makes the connection between the zwitterionic micellar layer closer. This is undoubtedly beneficial to the growth of micellar structure. Finally, this work explores the enhancement mechanism of the hydrophobic interaction and electrostatic interaction on the micelle structure.

Effect of temperature on the reverse self-assembly of lecithin and sugar alcohol mixtures in a nonpolar solvent

It has been shown that the addition of sugar alcohols to lecithin solutions induces a transformation from reverse spherical micelles into reverse cylindrical micelles, resulting in the formation of viscoelastic Maxwell fluids. Herein, we systematically investigated the effects of temperature on the rheological parameters, such as the plateau modulus (Gp), relaxation time (tR), and zero-shear viscosity (η0), of lecithin and sugar alcohol mixtures in decane. The rheological properties upon heating of mixtures of lecithin and sugar alcohols with different numbers (3–6) of hydroxyl (–OH) groups and concentrations were studied in detail. Gp, tR, and η0 for all reverse cylindrical micelles decreased with temperature. This decrease can be attributed to a reduction in the lengths of the reverse cylindrical micelles, as evidenced by the small-angle X-ray scattering results at different temperatures. More importantly, the decay rates of Gp, tR, and η0 upon heating decreased more rapidly when the hydrogen bonds between the lecithin and sugar alcohol molecules were weaker as the hydrogen bonds were closely associated with the formation of the reverse self-assembled structure. This indicates that the driving force for the formation of reverse cylindrical micelles can be weakened by increasing the temperature.

Anchorage-Dependent Living Supramolecular Self-Assembly of Polymeric Micelles.

Anchorage-dependent contact-inhibited growth usually refers to on-surface cell proliferation inhibited by the proximity of other cells. This phenomenon, prominent in nature, has yet to be achieved with polymeric micelles. Here, we report the control living supra-macromolecular self-assembly of elongated micelles with a liquid crystalline core onto a hydrophobic substrate via the synergetic interactions between the substrate and aggregates dispersed in solution. In this system, seed formation is a transient phenomenon induced by the adsorption and rearrangement of the core-swollen aggregates. The seeds then trigger the growth of elongated micelles onto the substrate in a living controllable manner until the contact with the substrate is disrupted. Brownian dynamic simulations show that this unique behavior is due to the fusion of the aggregates onto both ends of the anchored seeds. More important, the micelle length can be tuned by varying the substrate hydrophobicity, a key step toward the fabrication of intricate structures.

Determination of the Local Structure and the Persistence Length of Wormlike Micelles of Potassium Oleate by Small-Angle Neutron Scattering

Determination of the Local Structure and the Persistence Length of Wormlike Micelles of Potassium Oleate by Small-Angle Neutron Scattering

Constitutive modeling of dilute wormlike micelle solutions: Shear-induced structure and transient dynamics

We present a reformulation of the 'reactive rod model' (RRM) of Dutta and Graham [Dutta, Sarit and Graham, Michael D., JNNFM 251 (2018)], a constitutive model for describing the behavior of dilute wormlike micelle solutions. The RRM treats wormlike micelle solutions as dilute suspensions of rigid Brownian rods undergoing reversible scission and growth in flow. Evolution equations for micelle orientation and stress contribution are coupled to a kinetic reaction equation for a collective micelle length, producing dynamic variations in the length and rotational diffusivity of the rods. This model has previously shown success in capturing many critical steady-state rheological features of dilute wormlike micelle solutions, particularly shear-thickening and -thinning, non-zero normal stress differences, and a reentrant shear stress-shear rate curve, and could fit a variety of steady state experimental data. The present work improves on this framework, which showed difficulty in capturing transient dynamics and high-shear behavior, by reformulating the kinetic equation for micelle growth on a more microstructural (though still highly idealized) basis. In particular, we allow for micelle growth associated with strong alignment of rods and breakage due to tensile stresses along the micelles. This new formulation captures both steady and transient shear rheology in good agreement with experiments. We also find good agreement with available steady state extensional rheology.

Thermosetting supramolecular polymerization of compartmentalized DNA fibers with stereo sequence and length control

Thermosetting supramolecular polymerization of compartmentalized DNA fibers with stereo sequence and length control

Effect of pH on the Structure and Dynamics of Wormlike Micelles in an Amino Acid-Derived Surfactant Composition.

We studied the impact of pH as a thickening mechanism on the structure and dynamics of wormlike micelles in a mixture of sodium lauroyl sarcosinate (SLSar) and cocamidopropyl hydroxysultaine (CAHS). The viscoelastic properties were obtained using mechanical rheometry and diffusing wave spectroscopy, which provided access to a wide range of frequencies. By using a mesoscopic simulation method [Zou; Larson. J. Rheol. 2014, 58 (3), 681-721], characteristic micelle lengths and times were extracted including contour length, persistence length, entanglement length, reptation time, breakage time, breakage rate, and breakage rate constant. The interplay of pH-dependent reptation times (10-1000 ms) and breakage times (4-38 ms) leads to a minimum in the ratio of reptation time to breakage time of about 0.02 at pH 4.8. This minimum was closely associated with the sharp increase and decrease of the observed viscosity maximum at pH 4.8 in this system. These values may be contrasted with much longer breakage times (20-300 ms) that have been measured in more easily thickened sulfate-based systems. The low breakage times of the SLSar/CAHS system were attributed to the high and pH-sensitive breakage rate constants (0.01-0.17 ms-1 μm-1).

On the length of lecithin reverse wormlike micelles induced by inorganic salts: Binding site matters

Previous studies have shown that the addition of inorganic salts to lecithin organosols induces long wormlike micelles that lead to organogels. The viscosity of the micellar solution greatly increases with the increasing concentration of the inorganic salt until gelation, but interestingly, it dramatically drops after the gel regime. Although the growth mechanism has been rationally proposed, the reason for the decrease in viscosity remains unclear. In this study, we investigated the rheological behaviors and the self-assembled structures of the lecithin wormlike micelles induced by LiCl, CaCl2, and LaCl3 in cyclohexane. We found that the decrease in viscosity accompanies a shortening in the length of the wormlike micelles. Meanwhile, the study on the interactions between lecithin and the inorganic salts by FTIR shows that the inorganic salts move from the saturated phosphate and choline region to the ester linkage region on lecithin as the viscosity drops. We suggest the movement of the excess inorganic salts alters the effective molecular geometry, which in turn breaks the long wormlike micelle into short ones, thus causing the viscosity to decrease. In other words, the binding sites of the inorganic salts in lecithin headgroups is a key factor that determines the self-assembled structures of lecithin reverse micelles.

Small-angle X-ray scattering as an effective tool to understand the structure and rigidity of the reverse micelles with the variation of surfactant

This study is aimed to utilize the small-angle X-ray scattering technique for getting new insights on the effect of the structure of surfactants on the shape, size, thickness of the diffusion layer, and rigidity of the reverse micelles, formed within a water-in-oil microemulsion. For this study, two important features of the structure of the surfactant i.e. hydrophobic alkyl chain length and the nature of the hydrophilic head group (cationic, anionic, and non-ionic) are taken into consideration. The primary information regarding the shape, diffusion length, and internal structure of reverse micelles was evaluated using the model-free approach. It was found that the reverse micelles formed in the case of cationic and anionic surfactants were spherical whereas cylindrical-shaped reverse micelles were formed with non-ionic surfactants. After critically analyzing the inferences from the model-free approach, an appropriate model for fitting the SAXS data was selected. For cationic and anionic surfactant-based microemulsions, the spherical shell model was chosen while the cylindrical shell model was used for microemulsions formed using non-ionic surfactants. We believe that this study will give a systematic approach to analyze the SAXS data and further add to our understanding of the relation between the surfactant and the structure of the reverse micelles.

Investigating the influence of block copolymer micelle length on cellular uptake and penetration in a multicellular tumor spheroid model.

The efficient penetration of drug nanocarriers into tumors is an important prerequisite for therapeutic and diagnostic success. The physicochemical properties of nanocarriers, including size, shape and surface chemistry have been shown to influence their transport in biological systems. Recent studies have shown that elongated nanoparticles (NPs) can exhibit advantageous properties in comparison to spherical NPs, but these experiments have involved a variety of different materials, many of which are characterized by a broad size distribution. Here we describe a series of rigid rod-like micelles of uniform width, with narrow length distributions, and common surface chemistry, and examine their cell uptake and penetration into multicellular tumor spheroids (MCTSs) formed from two human breast cancer cell lines (MDA-MB-436 and MDB-MB-231). These micelles were prepared from a polyferrocenylsilane (PFS) diblock copolymer (BCP) with a corona block consisting of a statistical polymer of aminopropyl methacrylamide and oligo(ethyleneglycol methacrylate) (PFS27-b-PAPMA3-stat-POEGMA48). The rigid rod micelles, with a common width (12 nm) and lengths ranging from 80 to 2000 nm, were prepared by seeded growth crystallization-driven self-assembly in ethanol and then transferred to water. To consider whether changing the shape of these micelles affects its uptake and penetration behavior, analogous spherical micelles were prepared by direct nanoprecipitation into water. Both micelle shape and length were found to influence cellular uptake and penetration into 500 μm MCTSs. Laser confocal fluorescence microscopy was used to examine penetration of these micelles into three-dimensional MCTS up to 90 μm depth. Micelles with an elongated shape and short length (80 nm) demonstrated the deepest penetration into the MCTSs formed by MDA-MB-436 cells. Micelles with lengths of 200 nm also showed substantial penetration into these MCTS, but the extent and depth of tumor penetration of the rod-like micelles decreased with increasing aspect ratio. MCTS of MDA-MB-231 cells had a less dense, more open structure than those formed by MDA-MB-436 cells. Here more extensive penetration was observed, particularly for the longer micelle samples.

Regulating the morphology and size of homopolypeptide self-assemblies via selective solvents.

It remains a great challenge to control the morphology and size of self-assembled homopolypeptide aggregates. In this work, rod-like micelles including spindles and cylinders were prepared by a solution self-assembly of poly(γ-benzyl-l-glutamate) (PBLG) homopolypeptides with different degrees of polymerization, in which their size was controlled precisely by tuning the ratio of water/methanol in selective cosolvents. The length of the rod-like micelles increased with an increasing amount of methanol in the selective cosolvents, which was confirmed using the combination of SEM, TEM and AFM. The self-assembly mechanism of PBLG in selective cosolvents was investigated by using complementary Fourier transform infrared (FT-IR), circular dichroism (CD) and low-field NMR analyses. It was found that the shrinkage and swelling of PBLG chains play important roles in the self-assembly process. The obtained results may provide a guideline for the study of regulating the assembled aggregate sizes.

Determining threadlike micelle lengths from rheometry

We show that the average length ⟨L⟩ of threadlike micelles in surfactant solutions predicted by fitting results of a mesoscopic simulation, the “pointer algorithm,” to experimental G′(ω), G″(ω) data, is longer than, and more accurate than, that from a scaling law that equates ⟨L⟩/le to the modulus ratio G0/Gmin′′. Here, G0 is the plateau modulus, Gmin′′ is obtained at the local minimum in G″, and le is the entanglement length. The accuracy of the pointer algorithm is supported by the agreement of its predictions with results from a recent application of the slip-spring simulation method to threadlike micelles. Improved fits of the pointer algorithm to the slip-spring results are obtained for weakly entangled micelles (with an average number of entanglements of Z < 15) if the full spectrum of Rouse modes is included in the description rather than just the high-frequency modes included in an earlier version. For sodium laureth-1 sulfate and cocamidopropyl betaine in NaCl solutions, we find scaling relations for micelle length, the plateau modulus, and the persistence length that are in rough agreement with the predictions of mean field theory and with the modified scaling relation in which ⟨L⟩/le is raised to the 0.82 power, rather than unity, that we recommend as an improvement to the original scaling law.

The Relationship between Wormlike Micelle Scission Free Energy and Micellar Composition: The Case of Sodium Lauryl Ether Sulfate and Cocamidopropyl Betaine

The scission energy is the difference in free energy between two hemispherical caps and the cylindrical region of a wormlike micelle. This energy difference determines the logarithm of the average micelle length, which affects several macroscopic properties such as the viscosity of viscoelastic fluids. Here we use a recently published method by Wang et al (Langmuir 2018 34 1564-1573) to directly calculate the scission energy of micelles composed of monodisperse sodium laurylethersulphate (SLESnEO), an anionic surfactant. Utilising dissipative particle dynamics (DPD), we perform a systematic study varying the number of ethoxyl groups (n) and salt concentration. The scission energy increases with increasing salt concentration, indicating that the formation of longer micelles is favoured. We attribute this to the increased charge screening that reduces the repulsion between head groups. However, the scission energy decreases with increasing number of ethoxyl groups as the flexibility of the head group increases and the sodium ion becomes less tightly bound to the head group. We then extend the analysis to look at the effect of a common co-surfactant, cocamidopropyl betaine (CAPB) and find that its addition stabilises wormlike micelles at a lower salt concentration.